/* Medium
We have a list of points on the plane. Find the K closest points to the origin (0, 0).
(Here, the distance between two points on a plane is the Euclidean distance.)

You may return the answer in any order.
The answer is guaranteed to be unique (except for the order that it is in.)

Example 1:
Input: points = [[1,3],[-2,2]], K = 1
Output: [[-2,2]]
Explanation:
The distance between (1, 3) and the origin is sqrt(10).
The distance between (-2, 2) and the origin is sqrt(8).
Since sqrt(8) < sqrt(10), (-2, 2) is closer to the origin.
We only want the closest K = 1 points from the origin, so the answer is just [[-2,2]].

Example 2:
Input: points = [[3,3],[5,-1],[-2,4]], K = 2
Output: [[3,3],[-2,4]]
(The answer [[-2,4],[3,3]] would also be accepted.)

Note:
1 <= K <= points.length <= 10000
-10000 < points[i][0] < 10000
-10000 < points[i][1] < 10000

Relatives:
215. Kth Largest Element in an Array
324. Wiggle Sort II
347. Top K Frequent Elements
414. Third Maximum Number
692. Top K Frequent Words
703. Kth Largest Element in a Stream
973. K Closest Points to Origin
1471. The k Strongest Values in an Array
1985. Find the Kth Largest Integer in the Array */

#include <vector>
#include <queue>
#include <chrono>
#include <random>
#include <iostream>

using namespace std;

class Solution {
public:
    vector<vector<int>> kClosest(vector<vector<int>>& points, int K) {
        quickSelect(points, 0, points.size()-1, K);

        points.resize(K);
        return points;
    }

private:
    template<typename T>
    void quickSelect(T& data, int beg, int end, int k) { // [beg, end]
        if (beg >= end)
            return;

        auto pivot = partition(data, beg, end);
        if (pivot == k) {
            return;
        } else if (pivot > k) {
            quickSelect(data, beg, pivot-1, k);
        } else {
            quickSelect(data, pivot, end, k);
        }
    }

    template<typename T>
    int partition(T& data, int beg, int end) {
        auto pivot = dis(data[(beg + end) / 2]);

        while (beg <= end) {
            while (dis(data[beg]) < pivot)
                ++beg;
            while (pivot < dis(data[end]))
                --end;
            if (beg <= end)
                std::swap(data[beg++], data[end--]);
        }

        return beg;
    }

private:
    template<typename T>
    int dis(T& point) {
        return (point[0] * point[0] + point[1] * point[1]);
    }
};

namespace Iterator {

class Solution {
public:
    vector<vector<int>> kClosest(vector<vector<int>>& points, int K) {
        quickSelect(points.begin(), points.end(), K, [](const auto& lhs, const auto& rhs) {
            return (lhs[0] * lhs[0] + lhs[1] * lhs[1]) < (rhs[0] * rhs[0] + rhs[1] * rhs[1]);
        });

        points.resize(K);
        return points;
    }

private:
    template<typename Iter, typename Compare>
    void quickSelect(Iter beg, Iter end, int k, Compare cmp) { // [beg, end}
        if (beg + 1 >= end)
            return;

        auto pivot = partition(beg, end, cmp);
        auto dis = std::distance(beg, pivot);
        if (dis == k) {
            return;
        } else if (dis > k) {
            quickSelect(beg, pivot, k, cmp);
        } else {
            quickSelect(pivot, end, k - dis, cmp);
        }
    }

    template<typename Iter, typename Compare>
    Iter partition(Iter beg, Iter end, Compare cmp) {
        --end;
        auto pivot = *std::next(beg, getRandom<int>(0, std::distance(beg, end)));

        while (beg <= end) {
            while (cmp(*beg, pivot))
                ++beg;
            while (cmp(pivot, *end))
                --end;
            if (beg <= end)
                std::swap(*beg++, *end--);
        }

        return beg;
    }

    template<typename Size = int>
    Size getRandom(Size min, Size max) {
        std::random_device dev;
        std::default_random_engine engine(dev());
        std::uniform_int_distribution<Size> distribution(min, max);

        return distribution(engine);
    }
};

} // namespace Iterator

namespace Heap {
/* heap sort
 * Time complexity: heap sort O(NlogN) */
class Solution {
public:
    vector<vector<int>> kClosest(vector<vector<int>>& points, int K) {
        auto comparator = [](const auto& lhs, auto& rhs){
            return (lhs[0] * lhs[0] + lhs[1] * lhs[1]) > (rhs[0] * rhs[0] + rhs[1] * rhs[1]);
        };
        priority_queue<vector<int>, vector<vector<int>>, decltype(comparator)> priQue(comparator);

        for (const auto& point : points) {
            priQue.emplace(point);
        }

        vector<vector<int>> result;
        result.reserve(K);

        while (K--) {
            result.emplace_back(priQue.top());
            priQue.pop();
        }

        return result;
    }
};

} // namespace Heap

int main() {
    vector<vector<int>> points {
        {6373,4245},{1496,8228},{-3554,9008},{-5530,-6663},{4443,3262},{2179,-1675},{7450,-5056},
        {3752,9600},{1562,-9517},{1160,1963},{5499,7288},{2464,-7491},{-766,43},{-7764,3673},
        {-4120,2231},{-7344,-1001},{-1705,678},{-3112,-2648},{6822,3872},{1293,-6270},{8007,7524},
        {-3444,-6929},{702,-9840},{-318,-4201},{1240,6135},{-9425,-6953},{4064,-9950},{6563,1470},
        {-6264,-124},{-8972,-9927},{7664,3496},{5712,-79},{3351,-6827},{-4423,-206},{3995,-9457},
        {2894,906},{-4691,2740},{9863,-8647},{5881,-9184},{2144,9362},{-4060,-3030},{1588,1464},
        {-7051,3796},{1730,-6851},{-6895,-9803},{2430,5237},{9489,-2187},{6361,8977},{-266,-6456},
        {-2396,76},{-7770,-8626},{8419,1171},{-201,7660},{1861,2563},{7446,-2003},{-8370,-282},
        {5087,-5711},{-8935,6105},{786,-6103},{9319,5520},{-6774,-1890},{3659,-6955},{4817,4550},
        {2933,-1654},{4033,-103},{2516,9846},{4311,6102},{9986,9370},{8766,438},{3806,-9005},
        {-3822,-4287},{5866,-8144},{-7709,540},{-7450,4060},{734,8028},{7408,-962},{-5279,8320},
        {-388,-7582},{3685,8262},{2438,-5818},{-2561,-1010},{8446,2061},{9693,-5451},{5946,-4675},
        {4461,5569},{4408,5479},{8090,-889},{-772,5468},{-3595,3924},{-2741,9459},{8976,-6477},
        {5653,3405},{86,-1337},{-669,-9596},{-2703,-983},{959,3372},{9940,-8868},{2901,-4547},
        {2011,-5825},{8756,1670},{4001,-9163},{-1225,-7712},{-249,5851},{2376,7560},{275,-7899},
        {3582,5132},{-5525,-9815},{-572,-8763},{-5713,3870},{-3859,4728},{7885,-4919},{-2153,-7961},
        {4891,-620},{-314,6600},{5972,5045},{4162,9051},{9702,-2437},{-2868,-240},{-3037,4918},
        {9330,-3955},{5362,7522},{6027,5496},{500,321},{-6633,-7061},{2001,7837},{2257,-2401},
        {342,-4378},{3908,2518},{7569,63},{-4401,2012},{-5260,-4860},{-8382,-6748},{7813,1397},
        {2060,9806},{-9932,9794},{8653,-2796},{6068,-7067},{4884,-5303},{2771,4558},{1085,590},
        {-4785,-2323},{-5695,-4887},{-6441,-9972},{-2683,4961},{1754,-8291},{7098,7280},{-5258,-6220},
        {6023,-7110},{-9778,-1018},{-2829,8514},{-6520,-5075},{941,21},{-2338,-8916},{5903,2384},
        {-5937,7417},{-7063,9078},{8514,7207},{9010,-2519},{-1037,-5970},{8939,466},{-395,7659},
        {5085,-5773},{-2215,7526},{-3457,-7000},{5956,2240},{-1045,-6497},{-4941,5583},{-2128,-995},
        {-452,1926},{-1601,5981},{6303,-4572},{6360,-7723},{-9427,-1707},{8919,7137},{4355,3438},
        {9377,-4864},{5061,6201},{2379,3893},{-7416,2668},{5402,-6961},{8898,-5752},{9702,-9279},
        {7391,-1231},{-490,-1348},{3165,-2575},{4043,-1076},{8735,1595},{-3215,-7343},{5818,5172},
        {-48,-912},{-2142,-3469},{4840,-9922},{78,-7913},{300,-1116},{4173,8254},{4608,-2329},
        {-548,2059},{-5322,-6621},{-9265,6449},{6838,-7942},{-8377,4212},{-597,-1201},{1617,-4715},
        {-9703,1185},{-5620,-5379},{-9889,-2679},{440,-7345},{-1449,-9761},{4272,6166},{-9826,1672},
        {5253,6833},{-1014,-1729},{-3045,6815},{9371,-7046},{9699,-2822},{-2487,3113},{2796,444},
        {550,-8158},{4551,2151},{2619,9813},{-8166,-9556},{-1317,-4274},{8546,113},{-1678,9712},
        {-477,7260},{1534,-7106},{5739,2818},{-7222,-3243},{-2888,-5797},{5647,5935},{8398,9091},
        {-1235,5077},{9775,7314},{-3378,-1193},{-2340,-3542},{-4471,5977},{1328,2899},{-7903,-3778},
        {-1973,9219},{7202,2882},{4368,-7942},{-3904,9320},{-3130,7059},{1606,-7028},{2976,-4969},
        {9251,4200},{4426,5587},{-9960,-3549},{3395,4078},{-3369,3261},{3519,-9497},{2365,929},
        {8341,3135},{147,8798},{-1840,-5344},{3834,-300},{1003,4979},{-1120,169},{721,-10000},
        {-7408,1762},{-572,-9012},{-4251,-3449},{729,1888},{1516,-7558},{3231,-7267},{-4971,6162},
        {-1758,-9900},{-3849,-2878},{-4585,8189},{-1455,7364},{-5962,1075},{-1815,-2220},{948,301},
        {4933,2387},{5703,6374},{-2769,-4174},{6166,-9072},{-4422,6386},{325,-3655},{6664,7839},
        {4783,-9827},{-3246,3545},{3231,2613},{5546,-5199},{9024,7637},{7129,-643},{-6735,367},
        {2044,5201},{-245,8754},{-6021,-1504},{654,-1450},{4756,-1517},{-1718,-8584},{1170,8998},
        {-4141,-8371},{-7903,-3586},{6713,-1565},{726,-2987},{2491,-456},{9675,-7485},{-3211,1120},
        {6217,-5037},{-3690,-2945},{3751,-2557},{-2673,6557},{7795,-1954},{8358,5739},{-3445,1693},
        {-4161,-887},{7394,-9943},{2099,196},{7224,-8507},{-7878,-1084},{-2840,9251},{-9866,8439},
        {-7955,3050},{-7042,9100},{-8133,8570},{-6565,-2178},{-6009,-598},{-456,-1092},{7888,-8570},
        {6126,5388},{2858,-6545},{3528,5334},{-7578,4971},{-6058,-8349},{2654,4745},{1785,-5645},
        {-723,7282},{1823,9626},{-7448,-4186},{-9820,-4685},{-883,5951},{-5105,-1662},{-244,8276},
        {-2537,9855},{-9266,-1625},{1416,-8898},{-8820,5881},{-8748,-542},{-5854,-1330},{7132,-5684},
        {9523,-902},{-1349,-870},{-7224,9642},{-9831,-6146},{-3666,669},{5084,9013},{-8852,-3121},
        {-4551,8969},{-8987,-2850},{-8549,8637},{4299,-8361},{-2850,8992},{-8904,1865},{-9723,-1476},
        {229,-5653},{-7803,-807},{9973,1198},{-7474,4847},{-8076,9646},{2897,-1716},{-177,8930},
        {7569,9894},{4822,-6521},{1765,5916},{-5848,-6769},{900,-4013},{3135,-4586},{4866,1443},
        {-9794,7809},{-4364,-6686},{-4777,-6351},{2827,-9267},{-2392,5420},{-5001,-6934},{-5944,-2656},
        {-623,-3651},{-9809,-6460},{3901,2859},{9406,-5078},{-3119,2309},{6773,-3897},{2792,-4990},
        {6476,-2161},{-5226,4030},{5914,8250},{6606,8135},{1446,-6960},{6622,9762},{-2719,1149},
        {5073,-2548},{-5958,8614},{-4172,-3480},{3215,-773},{-4838,7389},{3584,-8352},{-6180,-4632},
        {-5633,2407},{-8564,-2646},{-5483,5630},{1658,-3534},{7850,-4980},{-9825,481},{3765,-1413},
        {4769,-9259},{-7695,-3625},{-1785,7633},{9995,2246},{-2270,3375},{-3501,5552},{-7193,-2633},
        {7662,-5707},{-9132,-9480},{-4242,6438},{-840,-2790},{4581,6991},{-6722,3961},{3983,-4473},
        {-8694,3921},{1629,-961},{8931,-1082},{4533,-7937},{5968,389},{1816,-2769},{3070,4461},
        {-6875,-9005},{9578,8076},{-3148,-1677},{5588,6195},{9432,1799},{-5598,-902},{4136,9532},
        {2657,-7204},{360,4571},{1351,2947},{2506,3094},{9288,-7954},{9251,5256},{6989,8223},
        {-4687,-2283},{-1348,-8334},{2867,354},{7412,246},{-2204,1674},{3953,4725},{-4274,-6472},
        {8123,-2872},{1742,8812},{1574,7345},{2582,-2305},{-5615,5456},{5723,556},{7038,-1354},
        {8786,-3225},{3198,-7354},{8926,-8371},{-117,-6004},{9026,-6361},{5050,7704},{5811,-413},
        {4755,7012},{-7377,297},{-1972,-2563},{6317,8022},{3123,4214},{489,-9726},{-774,3996},
        {3273,2987},{-4629,4130},{-1849,-4211},{-3732,7956},{-3093,2552},{-3319,-717},{6620,-5351},
        {1164,3547},{8218,-9999},{-5193,93},{1220,9328},{7323,6935},{167,7780},{-2529,6221},
        {6122,-2593},{7135,-8945},{4983,-199},{7632,3031},{-5405,8241},{-46,1349},{-2834,5244},
        {-4369,4424},{-672,-205},{7908,2391},{9492,2804},{5664,-1596},{-1103,1824},{5564,6789},
        {-3892,-5372},{8711,9385},{7469,8956},{185,-3370},{-117,-7507},{2532,6397},{7488,-9891},
        {2028,-1023},{-6853,-8549},{-7323,8435},{7320,-7133},{-2033,-1188},{-1971,-2613},{9537,2621},
        {-4572,-6563},{6074,7603},{-6100,1554},{-4631,157},{-5419,8242},{8384,-6686},{-3839,4974},
        {-3352,-5406},{-2071,3812},{-40,4332},{-5968,4187},{4639,-2767},{-3577,-2269},{5995,-2166},
        {3420,-918},{3207,7540},{3697,-6202},{-9752,1475},{-5112,-4831},{-4719,770},{-7789,7923},
        {3471,9744},{-4295,6218},{-1228,5758},{-5610,-6876},{-1762,-1348},{-2572,2929},{3199,4912},
        {8837,-9251},{9158,-9294},{3268,-883},{-5102,7969},{3537,2976},{-7364,159},{7394,-3286},
        {6520,-1912},{8654,-571},{2405,1765},{-6560,5707},{229,5716},{-432,-8624},{3120,-4102},
        {4344,51},{5105,7962},{-6433,-5008},{8045,7217},{-1345,-8787},{3900,8350},{3357,5090},
        {3470,648},{690,-7649},{-7352,4558},{-7350,7850},{-982,-9191},{6191,-6237},{-936,6321},
        {-8398,-5797},{-9998,1840},{-5686,-1909},{9543,4360},{-9827,-9818},{-4440,-4547},{-2212,-4498},
        {4313,9487},{1810,-2557},{3122,8527},{1615,8942},{7540,-812},{5540,-4247},{-2460,-5890},
        {-3180,5022},{3071,-6139},{9162,-6354},{5019,438},{-8398,928},{-1241,6786},{-1700,9509},
        {5426,6167},{-6167,5842},{-3226,7858},{-2269,8219},{-7071,3090},{4209,2917},{6142,-2774},
        {7155,-5464},{7175,5588},{6368,-6995},{-5240,1822},{-6119,9226},{456,-2191},{8635,3105},
        {-7655,-2013},{1941,-8006},{6303,9299},{9575,-8452},{1821,-2774},{2490,5227},{-2617,5532},
        {1343,2403},{-9964,2549},{6688,9879},{-5519,8671},{-6581,-8479},{5593,6782},{6601,3424},
        {-6648,-8714},{-4226,-8093},{1050,2267},{5437,-7710},{7848,6538},{-3766,3224},{-818,-4263},
        {6965,7135},{-2259,8186},{-1153,-661},{-8572,1611},{-3546,-3697},{-6938,5487},{-2248,1981},
        {-1596,-5553},{4103,2224},{2027,-4411},{-8897,-5316},{7741,-3096},{-5324,-1302},{-4489,244},
        {462,-1357},{6044,-9782},{4052,-6085},{2958,9089},{-2393,-1801},{-2675,9435},{4609,1864},
        {-8870,9697},{-1722,6280},{-3451,-7401},{7691,-4751},{-7114,9844},{-8790,9443},{1975,8680},
        {8053,-4172},{7416,8718},{5546,-7445},{2184,3518},{258,7703},{1045,-2641},{589,-3325},
        {342,8014},{-107,6039},{-458,7558},{6720,310},{-7265,1852},{-1088,-5587},{-7020,6934},
        {1401,6553},{-556,854},{-8326,-1619},{2426,988},{2080,8480},{171,4181},{2336,-910},
        {-5174,6426},{6504,9243},{-365,-5699},{2061,-2946},{-1278,-8216},{-8010,-8652},{7420,-8157},
        {7762,2895},{869,2364},{-5295,-4078},{7429,3293},{-8407,1066},{-2613,2415},{-6636,2593},
        {-5973,-1650},{-2295,2412},{-3179,7209},{-4766,8434},{-3148,7564},{-3347,4175},{-1035,2881},
        {5170,-6410},{7928,-7340},{-7852,-2338},{1349,3781},{7281,7168},{4697,-7236},{2797,-4722},
        {7707,3860},{-7133,-230},{-1350,5135},{-1685,-5133},{106,7719},{8263,-6842},{-139,1741},
        {-7667,4044},{6991,5811},{-5000,3587},{7981,3759},{7643,-4099},{9304,-9786},{5457,-5747},
        {4388,3531},{4020,-3672},{-1777,-3645},{728,2567},{-3800,-656},{9708,6724},{-3323,-4613},
        {7638,-6547},{2959,-4434},{-2415,-953},{8772,-3764},{1580,-1388},{8967,-8103},{-1154,3041},
        {-5806,-8116},{-2370,-5392},{7766,-2018},{-1431,-4966},{-682,8876},{-3372,8750},{-9906,-2543},
        {-1058,9102},{-1702,-9747},{-9518,-579},{8621,-1074},{2903,-1376},{-7899,-1414},{184,1396},
        {-1365,7313},{4647,-2403},{6940,-65},{8604,-311},{-1305,580},{7978,-990},{-9256,1050},
        {4702,-4294},{-2547,6630},{-4466,7580},{-3913,4747},{6171,633},{5076,3820},{-5867,-9365},
        {-7967,-5211},{-4671,-8767},{9363,9056},{-8148,-5619},{661,-6738},{-6899,-2743},{1527,-7042},
        {4915,660},{-8445,-2646},{-530,-9650},{1717,1902},{-4168,-7132},{-3306,-4603},{-9060,8889},
        {-9827,4295},{2039,-4295},{274,-2958},{4908,7933},{-6628,-5485},{-2888,-5067},{339,-8149},
        {-4434,6183},{6868,-1946},{-3545,9074},{-1188,678},{7823,-8292},{5916,-3556},{8046,-5852},
        {-2437,4731},{-5229,-5677},{-5931,-1297},{5932,-6626},{2717,-1605},{-6029,-4317},{1235,4065},
        {-3037,-6251},{-3095,-4962},{-1530,-6032},{-4565,5878},{9400,-3831},{-65,-3063},{2020,5578},
        {-4094,-5950},{7582,8638},{-6315,-4566},{5392,-4909},{9745,-5711},{5943,-3985},{887,3726},
        {2263,670},{6459,-4922},{-5430,4788},{-7352,3898},{3378,2319},{-8653,-6226},{3389,-2040},
        {3251,2809},{4335,251},{-5011,-5533},{3509,-6015},{-7049,-3405},{-6512,-4469},{8644,565},
        {4811,1608},{-7267,6935},{-2729,-1929},{6189,4126},{-7784,2618},{-6506,9578},{921,-8036},
        {-5497,-5983},{-5180,750},{1806,4728},{7360,-5455},{3888,2976},{-4135,-123},{-8474,-4420},
        {-8772,-3387},{9177,1602},{-9543,1689},{-502,3533},{8489,882},{-6266,-9411},{-4711,-4252},
        {3491,-1290},{-6546,-3002},{5384,-9684},{-4566,-9689},{-4102,-3731},{-8427,-746},{9257,-1132},
        {9091,1536},{-3866,872},{4021,6900},{-413,-1531},{5168,-1493},{5323,-6861},{3738,-3008},
        {362,-8853},{8861,2272},{-6901,-1582},{-3912,-5226},{-2050,-6602},{8609,-6176},{4716,2660},
        {9042,-201},{9551,1930},{1384,3678},{-3807,9558},{-1890,-1422},{-9871,4796},{1065,4204},
        {3793,2366},{3364,4756},{731,7235},{-164,7717},{6229,-4226},{-9696,-5156},{-9329,798},
        {-3059,-9650},{6698,4945},{-7702,-7113},{-9219,9429},{-1859,-6905},{-5617,6362},{-6988,-785},
        {-7648,-4336},{9958,8195},{-9985,-5870},{9701,8537},{-8443,-4508},{-799,9318},{-797,-3993},
        {2637,3650},{5918,1767},{8277,6815},{-5848,7334},{327,-1079},{3671,5861},{7330,8629},
        {-9717,-2083},{9771,2696},{-824,-312},{5652,9178},{-2734,8042},{-7970,-2302},{-3045,8087},
        {988,7531},{1424,-9143},{483,1017},{1470,-2896},{-5244,7887},{8525,5290},{-4434,-7942},
        {-348,595},{8054,-1799},{6534,8624},{-3386,5327},{5262,9135},{6123,9863},{-9157,955},
        {-1910,1652},{5533,4134},{-9947,-7322},{6794,8957},{2149,-2680},{-3236,2573},{7139,-1427},
        {-1144,-4006},{-9891,-6573},{8422,5459},{7681,-1127},{-1086,-58},{3288,-6682},{-6043,-5466},
        {4369,-9724},{-1048,3029},{5219,7797},{107,-5947},{3333,5893},{3128,2557},{-8539,-1340},
        {333,-8024},{7752,5393},{1227,6115},{3181,-4220},{-5246,-7310},{8993,4449},{-5478,-1651},
        {-1290,-8075},{617,-8665},{-5677,2152},{5964,3714},{-5314,8018},{-6237,-41},{-2134,-1670},
        {6685,-3774},{4019,2071},{6602,-4780},{-3699,-2068},{-5940,3871},{-6144,1415},{-7067,5814},
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        {-3218,-7523},{-2681,3771},{-781,-5764},{-8538,-7177},{-2023,1018},{5497,5},{-1472,6928},
        {375,-6883},{1439,8481},{960,-9009},{-2592,-4475},{-7019,3889},{-1669,6213},{2579,-7341},
        {4877,-5243},{5410,3274},{1275,-583},{-3632,-5640},{773,9748},{-1484,-1095},{1516,7899},
        {-5648,-4690},{-3053,-3825},{-8093,-8401},{-4770,-9167},{-4329,7997},{8643,-719},{-9718,694},
        {-9153,9433},{8381,-1059},{-7318,-585},{-3289,8851},{2492,-9120},{9707,4910},{-7198,9917},
        {6870,-2851},{-1461,3452},{-7648,2261},{-2293,9995},{7356,-7355},{8875,2593},{1263,8808},
        {-418,1890},{-3826,-1257},{6237,7424},{-3620,-1627},{-1730,7093},{2926,-4277},{-2869,-462},
        {-5516,8339},{3944,6471},{-5716,-5815},{8031,6445},{-4822,-6992},{-1340,4209},{128,6620},
        {-9145,6714},{-7862,3237},{6618,-721},{-55,8051},{-4905,-7252},{3207,6256},{9783,306},
        {1666,-8636},{8207,-7794},{9311,-2784},{-6410,4274},{2439,7476},{6705,-9807},{-3628,-2744},
        {1906,2927},{8328,-8342},{-3162,9909},{4869,-3757},{8296,3617},{-1188,-1087},{1729,-2806},
        {5025,8991},{4716,6056},{5916,8329},{2869,-2115},{-2429,1687},{-3666,6641},{-7385,-906},
        {9521,-8354},{9578,6483},{8859,-7906},{-8707,6221},{3442,-3921},{940,-3478},{206,-8865},
        {-6983,9992},{-7308,6533},{1924,7014},{8502,2115},{-5235,116},{5003,3761},{9064,5936},
        {3050,-9656},{6081,-1494},{704,7589},{-4347,-403},{3565,-6377},{2677,1824},{4096,-9808},
        {3697,-4377},{3225,-5258},{-6842,4189},{-2664,-9527},{-3697,3175},{-3806,9652},{6990,-2476},
        {3709,-620},{-8372,7806},{-9492,-2069},{5751,-1493},{6518,-6794},{4096,-1211},{-8080,8805},
        {-264,4059},{9148,-1314},{-235,-34},{7972,3953},{-8059,-2009},{8602,-816},{8509,4514},
        {-844,4430},{-5561,-1311},{6017,-4832},{6114,-4634},{-6081,-1094},{6669,-3561},{6757,-6313},
        {-2752,-6129},{6896,8235},{7158,6660},{-1018,5807},{7920,-957},{-205,-3142},{7195,4704},
        {9606,1155},{-7726,2296},{4725,4119},{6670,3954},{-8662,-7611},{-4961,9011},{-922,-6842},
        {-8283,-1553},{-259,-5403},{1648,4942},{3783,4631},{-8305,2838},{-4051,-8391},{8087,-7818},
        {-1247,-3625},{-7064,-3688},{4214,-4309},{-6227,-9201},{-1788,8408},{-5374,-8850},{8763,8241},
        {2810,-1266},{-6196,5943},{8424,-4166},{-5508,-2079},{-2401,5096},{-5967,-9727},{-7236,8334},
        {1040,-8240},{-5110,-5796},{-4945,2891},{-2836,-9613},{1647,1908},{8980,-467},{3017,7875},
        {-4611,9303},{2462,-8403},{8221,1314},{-9362,-1471},{4501,-7621},{-7420,8237},{-9156,-5892},
        {8875,-2173},{5606,-9452},{5969,-2803},{7437,7416},{6779,5051},{-7125,-1063},{39,5130},
        {6501,9442},{-7963,-3311},{-8779,-2990},{-9059,-6462},{-391,-3850},{-3513,-4813},{-9004,-9983},
        {-6495,1318},{833,8527},{9357,1847},{-9530,-9749},{-8621,6889},{-6932,-7514},{-43,-9668},
        {-2535,-4895},{-8064,-1914},{-4339,-8027},{-1827,-5972},{-3550,-5191},{2889,-5647},{-7916,1653},
        {-1257,3546},{1268,2839},{4878,1498},{-8526,-3245},{-1515,6614},{7455,-6094},{-9805,-245},
        {6016,-786},{-3895,4525},{6122,-7603},{-6923,6438},{-7731,-3606},{-8174,-4091},{2600,7108},
        {4200,-8146},{-4281,180},{6140,-1934},{311,-3686},{5635,9410},{-2796,9068},{7678,6842},
        {4812,2550},{618,-5242},{-6356,-8070},{1624,1300},{-4767,-5223},{-9252,-7386},{2437,-6450},
        {8104,-4668},{-6177,952},{-464,7810},{-2576,8570},{-7775,-9539},{8722,-420},{43,9786},
        {-464,-6503},{3445,702},{9061,1692},{5589,-2281},{4487,3737},{-3511,5564},{9876,-5987},
        {8644,-7073},{6125,-6775},{5735,5115},{-4722,7126},{-7783,4273},{4121,-7064},{-6093,2441},
        {-5245,-3279},{-1701,-8736},{5496,-7745},{1892,-8393},{-4504,-809},{-4944,2732},{7191,-5382},
        {6155,1905},{9592,3584},{3950,2985},{8714,1004},{-8821,-7136},{3979,3704},{-7321,6400},
        {2177,2666},{-8278,7999},{-7852,-2986},{-4307,-235},{9639,4047},{4062,9900},{3571,-1188},
        {5524,3505},{2324,8373},{-5985,7974},{-6428,-9202},{1417,2333},{-5427,1978},{6073,4374},
        {-4328,-17},{8303,2073},{-6686,7702},{-1741,-5134},{8832,-9988},{-1182,-686},{-1214,363},
        {-9121,-243},{1260,-5162},{3565,-6},{-3813,-5084},{6753,4644},{8492,2503},{3500,-271},
        {-2912,828},{3029,-8835},{-5408,-5202},{-1650,-5386},{739,-5438},{7957,6331},{-8068,-9690},
        {993,-4660},{3256,9546},{1132,988},{9267,6013},{-9623,-6670},{4811,3152},{-2381,773},
        {8001,-8661},{4356,-5014},{5567,4942},{7559,-246},{7285,4881},{-1357,-5294},{-8835,4753},
        {5869,4421},{610,1439},{4960,-3525},{2262,8185},{-2463,-1648},{-7680,-8731},{-7189,2997},
        {6918,3847},{5763,5038},{-12,-8531},{320,-780},{665,9815},{-8192,400},{-9345,-2654},
        {-6651,8770},{9962,-7448},{1754,3503},{-270,-1490},{-7145,-8882},{8861,-4619},{7704,7165},
        {-3634,-4631},{7757,5814},{8235,9811},{-6863,1091},{-4107,4918},{5898,325},{-5616,-4508},
        {-1064,6463},{2061,-533},{-8525,-8603},{8308,6487},{3247,-6658},{-4792,8810},{-3408,4608},
        {-677,6764},{4109,4957},{3956,5865},{2248,-4781},{-7914,9808},{-8124,9961},{-9211,-9249},
        {-6606,663},{-4655,9456},{-2851,2576},{1354,-5930},{632,7771},{6572,-858},{3330,-4562},
        {886,5017},{8682,-8015},{1100,6680},{1817,1616},{-6437,9468},{-1318,2265},{-8941,445},
        {3506,-3044},{4402,-3896},{-9376,-2876},{3863,2224},{6492,2131},{4237,-426},{-4470,-9532},
        {-1770,586},{-9917,-6900},{-3463,-2028},{6185,-9891},{2266,-8641},{4506,-6765},{-9819,-1378},
        {-7530,-1311},{-1208,8830},{-2712,1318},{-2494,-5338},{-3446,-1134},{2602,1227},{-9821,-3728},
        {3706,-3070},{1078,-8395},{-1708,-3571},{-3473,7401},{487,-3870},{8866,594},{8553,4521},
        {-7110,1123},{3102,9161},{-7596,-3245},{-3595,-6416},{-2618,-2602},{-728,7289},{4622,-7279},
        {-8767,-9321},{2789,-1242},{5908,-515},{7356,-8252},{7031,-7119},{-2265,9735},{8094,-1640},
        {5303,-9805},{-8231,-8336},{-5248,8919},{1820,-3384},{-3562,-9227},{7769,-3165},{-4928,759},
        {-7484,3302},{-3726,8898},{7995,5721},{-611,-7419},{3145,-1633},{-2475,-7189},{8684,-9753},
        {1822,2586},{-891,-5911},{6965,3394},{7442,-7385},{-7694,-5802},{-3163,-9187},{-9254,-9949},
        {4281,9370},{2080,-979},{2567,-7073},{8001,8752},{-3588,8520},{1393,-2832},{9987,3062},
        {4148,6159},{1498,5290},{7092,-3954},{8922,3200},{1207,4485},{-2130,3500},{8656,-3358},
        {6232,9293},{1015,-96},{-9977,1067},{8941,-2955},{4264,6053},{-4326,3252},{-881,941},
        {4029,7631},{-2724,3968},{-8217,-6459},{1677,-1414},{3968,-7635},{1604,882},{233,5230},
        {1249,9093},{7762,9743},{-8675,7649},{6726,2528},{8910,4480},{101,191},{-9505,2127},
        {3403,-1204},{7583,1548},{-9403,-1182},{7438,-745},{9206,-365},{-7040,-463},{-4687,-8440},
        {-8928,-5955},{795,3213},{-2409,-4227},{3022,6220},{-4165,9785},{914,4444},{7986,5203},
        {4159,9951},{-9196,-3532},{-2553,-5608},{7903,-6032},{-7184,-2329},{4469,9747},{2150,-8225},
        {9334,-1920},{7516,2957},{-7491,-1519},{758,6418},{-6226,-6833},{4784,-686},{-6221,6667},
        {-679,6971},{-317,-7167},{480,1884},{7677,769},{2173,-853},{5402,-7803},{921,-238},
        {-8415,5011},{9590,-4453},{-9211,-1810},{7020,6610},{6507,-6264},{3805,-5282},{620,6891},
        {-2901,-9703},{7269,-8494},{-7989,7044},{710,178},{8058,8556},{1229,-517},{9626,2678},
        {-3734,6043},{8267,6127},{735,-9140},{8639,7041},{7843,1784},{-6872,4578},{-6528,9138},
        {1583,-7035},{-1154,-4284},{6911,-9925},{-8951,-1078},{-247,444},{4250,7012},{1489,-4679},
        {-6738,-6291},{-6502,-6494},{-1332,6345},{-3641,2500},{9476,-3470},{-8472,263},{926,-665},
        {1600,-8577},{-9807,5007},{-8957,-4234},{-5384,-6847},{3015,-5680},{-6579,9911},{472,-3425},
        {9113,9176},{672,1065},{-6958,7389},{-4717,2749},{4705,-3508},{-9194,8067},{-9769,3380},
        {5680,-2404},{7223,1257},{-5032,-5008},{-5461,-7203},{4299,-2436},{-9631,-8620},{7455,-6946},
        {4942,3227},{7920,9843},{-7660,-8490},{465,-4738},{9702,360},{1898,-754},{8091,-4129},
        {9944,4302},{-1099,-6899},{-8470,-1316},{-1356,8885},{3810,-6409},{1730,6929},{2960,-737},
        {-1529,7416},{-3316,124},{2325,-3132},{5856,-6135},{687,-341},{-2126,8356},{2944,9422},
        {-6810,3161},{9545,-5758},{1959,2769},{-3232,7449},{-6370,-5108},{-8650,-5779},{-387,5766},
        {2490,4420},{5583,-7209},{217,1164},{8154,295},{6556,-4692},{4803,-2196},{-6678,-7608},
        {1826,5973},{-9563,-2031},{9544,6237},{-3298,-2844},{-9859,-430},{2130,4897},{-2696,7324},
        {8436,6738},{-4311,5343},{-6888,5985},{-4007,-7334},{6206,-2958},{6263,8437},{6359,-2269},
        {-1239,-8445},{8183,802},{7942,2430},{-200,-8134},{9145,-8086},{-8687,5388},{1512,-5882},
        {8005,8712},{2222,-2495},{-3826,6523},{-2797,-968},{616,-2414},{4368,394},{1542,1641},
        {1064,5186},{3857,665},{4376,6173},{1357,-2864},{-4687,682},{-8679,-8816},{8345,-3755},
        {-1859,2976},{-582,755},{-5548,-8581},{-4968,-4189},{-7330,-1913},{493,-3496},{-7713,6677},
        {5972,9802},{-3793,6362},{-9078,581},{7387,-2179},{1301,-5622},{-8301,5316},{-3195,6937},
        {4759,-2517},{1804,-6340},{-1625,740},{9574,-5777},{5726,496},{6807,-5004},{673,2992},
        {6708,-8360},{-5983,-2123},{-211,-610},{-9926,8372},{6176,3688},{7074,-4759},{6260,-3151},
        {-3447,9516},{466,7864},{4580,-9512},{-1109,5031},{-6208,-6057},{1065,165},{-9536,-2559},
        {-6771,1803},{2354,-8348},{7412,-4891},{-9285,-7694},{7307,1622},{845,-2631},{-1778,-6018},
        {-8558,-328},{-1073,-3140},{3357,-9657},{-3150,4203},{6068,-4498},{-6125,-1743},{-5075,-1375},
        {-6365,-1214},{59,1982},{9573,2866},{2799,-2321},{-3236,6711},{5594,6525},{6800,-6539},
        {8243,9557},{517,-8522},{-2428,-1554},{6718,-7882},{-9413,-848},{9697,-7642},{-4289,7784},
        {-1110,-1360},{7609,-8458},{-2918,-3845},{-1812,-9772},{-1563,-4131},{-6324,2234},{31,2181},
        {-4160,8},{-119,-5793},{9035,-7316},{9041,279},{-8780,-2398},{-847,107},{5447,7265},
        {-3911,2871},{-2945,-4159},{2862,-5141},{-4138,-8192},{-2530,3342},{-543,8838},{6360,624},
        {-7876,3928},{-3058,-7328},{7074,792},{-6255,1677},{9327,4060},{7518,793},{-2206,-4317},
        {4221,9890},{2523,9198},{9237,-8529},{1005,-9381},{5030,-6772},{-1782,6174},{-2736,-6666},
        {-9465,-7336},{4572,119}
    };

    Solution s;
    auto i = 0;
    for (const auto& d : s.kClosest(points, 5313)) {
        std::cout << ++i << " ";
        copy(d.begin(), d.end(), ostream_iterator<int>(cout," "));
        std::cout << std::endl;
    }
}